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PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees

Jonas Rothfuss · Vincent Fortuin · Martin Josifoski · Andreas Krause

[ Abstract ] [ Livestream: Visit Reinforcement Learning 15 ] [ Paper ]
Thu 22 Jul 5:25 a.m. — 5:30 a.m. PDT
[ Paper ]

Meta-learning can successfully acquire useful inductive biases from data. Yet, its generalization properties to unseen learning tasks are poorly understood. Particularly if the number of meta-training tasks is small, this raises concerns about overfitting. We provide a theoretical analysis using the PAC-Bayesian framework and derive novel generalization bounds for meta-learning. Using these bounds, we develop a class of PAC-optimal meta-learning algorithms with performance guarantees and a principled meta-level regularization. Unlike previous PAC-Bayesian meta-learners, our method results in a standard stochastic optimization problem which can be solved efficiently and scales well.When instantiating our PAC-optimal hyper-posterior (PACOH) with Gaussian processes and Bayesian Neural Networks as base learners, the resulting methods yield state-of-the-art performance, both in terms of predictive accuracy and the quality of uncertainty estimates. Thanks to their principled treatment of uncertainty, our meta-learners can also be successfully employed for sequential decision problems.

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